Compared to the algorithm of Lamprinakou et al. [1]}, the computational cost of the propagation step (step 12 of KDPF) increases, taking into account the age band of an individual due to the cost of finding the probabilities \(\lbrace P(a)\rbrace _a\) , that is, \(O(|\mathcal {A}|)\)  with \(|\mathcal {A}|\)  being the cardinality of the set of age bands \(\mathcal {A}\) . However, the increase is negligible even if we consider 200 age groups. For this reason, the computational costs of propagation (step 12 of KDPF) and finding weights (step 14 of KDPF) at state (interval) \(j\)  remain equal at \(O\left(N\sum \limits _{v=j-\eta }^j|S_v^N|\right)\) . The computational cost of finding auxiliary weights (step 9 of KDPF) at state (interval) \(j\)  is the combined costs of propagation and finding weights. Hence, the computational cost of the algorithm over all states (intervals) is \(O\left(N\left(\eta +1\right)|\mathcal {T}^N|\right)\) . \(N\)  is the number of particles, \(S_j^N\)  the set of latent cases falling into subinterval \(\mathcal {T}_j\) , \(\mathcal {T}^N=\cup _{j}S_j^N\)  and \(\eta \)  the number of former subintervals that influence the latent cases falling into \(\mathcal {T}_j\)  determined by the transition kernel of latent cases. The \(O\) -notation denotes the asymptotic upper bound [2]}. The algorithm is easily parallelized over \(N\) . We note that accounting for each person's age band does not increase the algorithm's complexity.
